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초록
In this paper, we prove that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer n ≥ 2 (Formula presented) holds for all x1, …,xn ∈ V. Let V, W be real vector spaces. It is shown that if a mapping f: V → W satisfies (Formula presented) or (Formula presented) for all x1, …, xn ∈ V, then the mapping f: V → W is Cauchy additive-quadratic. Furthermore, we prove the Hyers-Ulam stability of the above quadratic functional equations in Banach spaces.
키워드
Hyers-Ulam stability; Inner product space; Quadratic functional equation; Quadratic mapping; Banach spaces; Computation theory; Functional analysis; Mapping; Molecular physics; Nonlinear equations; Fixed integers; Hyers-Ulam stability; Inner product; Inner product space; Quadratic functional equations; Quadratic mapping; Real vector space; Vector spaces
- 제목
- Inner product spaces and quadratic functional equations
- 저자
- Park, C.; Park, W.-G.; Rassias, T.M.
- 발행일
- 2016-00
- 유형
- Conference Paper
- 저널명
- Springer Proceedings in Mathematics and Statistics
- 권
- 155
- 페이지
- 137 ~ 151